Channel estimation and equalization are important determinants of the quality of achieved data throughput in a digital communication system receiver. In conventional receivers, channel estimation is often performed using a technique known as Least-Mean-Squares (LMS) estimation, while channel equalization is performed using Maximum-Likelihood (ML) sequence detection via the Viterbi algorithm. A problem with these existing techniques is that, in their original form, they generally require many complex multiplication operations. More particularly, LMS estimation requires 2M multiplications, and a full-search Viterbi algorithm requires PM multiplications, where M is the order of the channel estimator, and P is the size of the symbol alphabet. The large number of multiplications may render these conventional estimation and equalization techniques prohibitively expensive in terms of the required computational resources, particularly at very high data rates.
Subsequent implementations of the LMS estimation technique have attempted to reduce the required number of multiplications through the use of signed approximations of a regression vector and/or an error signal, as described in, e.g., T. A. C. M. Claasen and W. F. G. Mecklenbräuker, “Comparison of the convergence of two algorithms for adaptive FIR digital filters,” IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. ASSP-29, No. 3, pp. 670-678, June 1981; D. L. Duttweiler, “A twelve-channel digital echo canceler,” IEEE Trans. on Communications, Vol. COM-26, No. 5, May 1978; and R. D. Gitlin, J. E. Mazo and M. G. Taylor, “On the design of gradient algorithms for digitally implemented adaptive filters,” IEEE Trans. on Circuit Theory, Vol. 20, No. 2, pp. 125-136, March 1973. These non-linear methods, however, can alter the training behavior such that the training speed is considerably reduced. As a result, these methods are typically suitable for use only in applications in which long training sequences are available, e.g., broadcasting applications.
It has also been proposed that pipelining be introduced in order to increase the throughput of the implemented hardware, as described in, e.g., M. D. Meyer and D. P. Agrawal, “A modular pipelined implementation of a delayed LMS transversal adaptive filter,” Proc. of ISCAS, New Orleans, pp. 1943-1946, 1990. A pipelining technique, however, leads to delayed updates that also corrupt the learning behavior of the LMS algorithm. See, e.g., P. Kabal, “The stability of adaptive minimum mean square error equalizers using delayed adjustment,” IEEE Trans. on Communications, Vol. COM-31, No. 3, pp. 430-432, March 1983; G. Long, F. Ling and J. A. Proakis, “The LMS algorithm with delayed coefficient adaptation,” IEEE Trans. on Acoustics, Speech and Signal Processing, Vol. ASSP-37, No. 9, pp. 1397-1405, September 1989; and G. Long, F. Ling and J. A. Proakis, “Corrections to ‘The LMS algorithm with delayed coefficient adaptation’,” IEEE Trans. on Signal Processing, Vol. SP-40, No. 1, pp. 230-232, January 1992.
Although a number of techniques have been developed to compensate for the above-noted corruption, e.g., as described in M. Rupp and R. Frenzel, “The behavior of LMS and NLMS algorithms with delayed coefficient update in the presence of spherically invariant processes,” IEEE Trans. on Signal Processing, Vol. SP-42, No. 3, pp. 668-672, March 1994; and E. Bjarnason, “Noise cancellation using a modified form of the filtered-XLMS algorithm,” Proc. Eusipco Signal Processing V, Brüssel, pp. 1053-1056, 1992, such techniques often require even more multiplications. Straightforward realizations of delayed-update LMS with compensation are described in T. Kimijima, K. Nishikawa and H. Kiya, “A pipelined architecture for DLMS algorithm considering both hardware complexity and output latency,” Proc. Eusipco, Patras, Greece, pp. 503-506, September 1998.
As is apparent from the above, a need exists for improved channel estimation, channel equalization and other signal processing techniques, which can eliminate or substantially reduce the required number of multiplications, without significantly altering training behavior, numerical precision or other desirable attributes of the corresponding algorithms.